Pythagorean Theorem Word Problems

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: c² = a² + b².

Front

How do you find the length of the diagonal in a rectangle?

Back

To find the length of the diagonal (d) in a rectangle, use the Pythagorean Theorem: d = √(length² + width²).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is twice the shortest side.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you apply the Pythagorean Theorem to real-world problems?

Back

Identify the right triangle in the problem, label the sides, and use the Pythagorean Theorem to find the unknown side.

Front

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance (d) between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a rectangular field is 50 yards wide and 100 yards long, how far is it from one corner to the opposite corner?

Back

Using the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √12500 = 111.80 yards.

Front

What is the length of a ramp that is 5.25 ft tall and 25.75 ft long?

Back

Using the Pythagorean Theorem: d = √(5.25² + 25.75²) = √(27.5625 + 665.0625) = √692.625 = 26.28 ft.

Front

How long is the diagonal of a piece of paper that is 11 inches tall and 8 inches wide?

Back

Using the Pythagorean Theorem: d = √(11² + 8²) = √(121 + 64) = √185 = 13.60 inches.